Question

two ways of making a complex part are possible: (1) using the sophisticated machines and the more sophisticated laborers, who earn about $25 an hour ;or (2) several unsophisticated machines in sequence using unsophisticated labor, earning $10 an hour. How much faster does (1) need to be compared to (2) for (1) to be the better method

Answer 1

2.5 times faster

Explanation:

The cost per hour of method 1 is $25, while the cost per hour of method 2 is $10. In order for method 1 to be the better method, it must have a productivity, in units per dollar, that is equal or greater than the productivity of method 2:

`A(units)/(hour) *(hour)/(\$25) \geq B(units)/(hour) *(hour)/(\$10)\\0.04A\geq 0.1B\\A \geq 2.5 B`

The productivity A of method 1, in units per hour, must be 2.5 times greater than the productivity of method 2, which means that method 1 needs to be 2.5 times faster than method (2) to be the better method.